An Improved Gradient Projection-based Decomposition Technique for Support Vector Machines

In this paper we propose some improvements to a recent decomposition technique for the large quadratic program arising in training support vector machines. As standard decomposition approaches, the technique we consider is based on the idea to optimize, at each iteration, a subset of the variables through the solution of a quadratic programming subproblem. The innovative features of this approach consist in using a very effective gradient projection method for the inner subproblems and a special rule for selecting the variables to be optimized at each step. These features allow to obtain promising performance by decomposing the problem into few large subproblems instead of many small subproblems as usually done by other decomposition schemes. We improve this technique by introducing a new inner solver and a simple strategy for reducing the computational cost of each iteration. We evaluate the effectiveness of these improvements by solving large-scale benchmark problems and by comparison with a widely used decomposition package.     

An optical measurement of vortex shape at a free surface

We have proposed an optical method of vortex shape measurement based on Fourier transform profilometry (FTP) and verified it by experiment. The results of our experiment proposed in this paper show that FTP can efficiently reconstruct the vortex shape at a free surface and this method is suitable for wide use in studying such problems as liquid shear flow, wake of an object, flow behind a bluff body, and wetting angle.     

准晶体中八方晶系点群的对称性与矩阵表示

从理论上对准晶体中八方晶系各点群进行了研究.运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表.运用坐标变换和群论在自定义的八方坐标系中,推导出八方晶系点群所有对称操作的矩阵.这32个3×3矩阵的结构是相当简洁的,它们的矩阵元只有5种可能取值:0,±1,±2.其中2是反映八方晶系准晶体所具有的准周期性的特殊无理数.     

在一个新步长规则下梯度投影算法的全局收敛性

考虑约束最优化问题：minx∈Ωf(x)其中:f:R^n→R是连续可微函数，Ω是一闭凸集。本文研究了解决此问题的梯度投影方法，在步长的选取时采用了一种新的策略，在较弱的条件下，证明了梯度投影响方法的全局收敛性。     

一个线性约束优化问题的广义梯度投影法

本文对线性约束优化问题提出了一个新的广义梯度投影法，该算法采用了非精确线性搜索，并在每次迭代运算中结合了广义投影矩阵和变尺度方法的思想确定其搜索方向．在通常的假设条件下，证明了该算法的整体收敛性和超线性收敛速度．     

线性均衡约束最优化的一个广义投影强次可行方向法

本文讨论带线性均衡约束最优化问题,首先利用摄动技术和一个互补函数将问题等价转化为一般约束最优化问题,然后结合广义投影技术和强次可行方向法思想,建立了问题的一个新算法.算法在迭代过程中保证搜索方向不为零,从而使得每次迭代只需计算一次广义投影.在适当的条件下,证明了算法的全局收敛性,并对算法进行了初步的数值试验.     

采用MSDI严格角动量投影46Ti、48Cr形变HF谱

采用修正的表面δ相互作用(MSDI),以球形壳模型单粒子态作基矢,对fp壳层区偶偶核⁴⁶Ti、⁴⁸Cr进行形变Hartree–Fock(HF)计算,并用形变HF单粒子态构造Slater行列式波函数,即形变HF内禀态,然后对其实施严格角动量投影程序,得到比较合理的结果.     

广义分解定理与两个不等式

本文给出了Banach空间广义分解定理的一个初等证明,并利用它来证明两个对称不等式.这是首次在Banach空间获得这样的不等式.     

基于CCD采集的Mach-Zehnder干涉条纹图的处理算法

Mach-Zehnder干涉仪适用于研究气体密度迅速变化的状态。由于气体折射率的变化与其密度的变化成正比,而折射率的变化将使通过气体的光线有不同的光程,因此可通过干涉臂变化对干涉条纹图像效果的影响得到气体密度。实测中,采用图像采集卡和CCD来接收Mach-Zehnder干涉仪产生的条纹图像,再通过计算机对条纹图像的条纹间距进行处理,从而得到气体密度的变化状态。从光干涉理论出发,对Mach-Zehnder干涉条纹图像特征进行了分析,建立了Mach-Zehnder干涉条纹的数学模型,并根据此模型设计了处理Mach-Zehnder干涉条纹图像的算法。算法包括图像的预处理(即图像的噪声提取)、图像的二值化及图像的细化。     

Mackey Theory for p-adic Lie Groups

This paper gives a p-adic analogue of the Mackey theory, which relates representations of a group of type G - H × t A to systems of imprimitivity.